New Method Gives Correct Simulation
Results of Maxwell's Equations at All Frequencies

Robert Adams (Ph.D.,
'98) is the first person to develop an elegant method of simulating
Maxwell's equations with consistently stable and correct results
in all frequencies.

Consistently stable and accurate computer simulations of Maxwell's
equations at all frequencies are now possible with a new method
developed by Robert Adams (Ph.D., '98), a research assistant
professor with the department's ElectroMagnetic
Interactions Laboratory (EMIL).

Since the advent of computer analysis, engineers and scientists
have struggled to get accurate numerical solutions to Maxwell's
equations. These computational difficulties have limited the
practical usefulness of numerical simulation methods for electromagnetic
phenomena, Adams said.

"Conventional simulations of Maxwell's equations are unstable
as the frequency gets low. A number of people have published
incorrect results as a consequence," he said. "Surprisingly,
these low-frequency instabilities also prevent the accurate and
efficient simulation of high-frequency field behaviors."
"There is nothing wrong with traditional formulations of
Maxwell's equations - until we simulate them on finite-precision
machines," he said.

According to Adams, researchers have been performing numerical
simulations using the classical representations of Maxwell's
equations found in most textbooks. "In many cases, these
formulations are ill-posed," he said. The traditional formulations
can be patched-up to extend their ranges of validity, "but
the biggest problem is that we usually don't know when this ad
hoc approach will break. It becomes difficult to have confidence
in the results of a simulation."

The ill-posedness of the original formulations is a problem at
all frequencies, he said, but it becomes particularly acute at
low frequencies. "We've developed a single formulation that
is uniformly well-posed at all frequencies. People have previously
developed different approaches for different frequencies, but
ours works gracefully in all ranges," he said.

When discussing low frequency, Adams is referring to the size
of an object relative to the electromagnetic wavelength. His
results will be useful to anybody simulating scalar and vector
wave phenomena.

The Bradley Department of
Electrical and Computer Engineering
Virginia Tech